Cups per Kilogram: A Home Rehydration Dosing Rule with the Cup-Size Error Left In

When an infant loses fluid through diarrhoea, the volume to be replaced is set by body weight: a stated deficit of 30 mL/kg for a mild loss, 75 mL/kg for a moderate loss, and 100 mL/kg for a severe loss. At home that volume is not measured in millilitres. It is counted in cups. This paper derives a dosing rule in household cups per kilogram — for the moderate deficit, 0.3125 nominal cups per kilogram over four hours, at 18.75 mL/kg per hour, below a stated oral intake rate limit of 20 mL/kg per hour — and then, instead of assuming the cup is the 240 mL it is called, leaves the cup-size error in the model. Real household cups are modelled with a mean volume of 250 mL and a standard deviation of 50 mL. A caregiver who counts cups as if each were 240 mL delivers, on average, 104.4% of the target, but with a standard deviation of 20.4%: 24.7% of modelled cases under-deliver by more than the study's stated material margin of 10% of the target (more than 7.5 mL/kg short at the moderate target), and 12.2% under-deliver by more than 20%, while 39.0% over-deliver by more than 10%. For a 5 kg infant at the moderate target of 375 mL, the 5th percentile of delivered volume is 262 mL. A one-time calibration step — filling the cup once from a bottle of known 500 mL volume and marking or counting the fill — reduces the delivered-volume standard deviation from 20.4% to 3.9%, a 5.2-fold reduction, and reduces the fraction under-delivering by more than 10% from 24.7% to 0.43%. The paper prints the rule's stopping point at full size: a deficit at or above the severe band, or an infant who cannot drink, vomits repeatedly, shows signs of shock, or does not improve, is outside home dosing altogether, and the rule must not be used to delay seeking care.